Expression of type And

from the theory of proveit.numbers.divisibility

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import a, b, k
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Complex, Divides, Mult, zero

# build up the expression from sub-expressions
expr = And(InSet(a, Complex), InSet(b, Complex), InSet(k, Complex), Divides(Mult(k, a), Mult(k, b)), NotEquals(k, zero))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(a \in \mathbb{C}\right) \land \left(b \in \mathbb{C}\right) \land \left(k \in \mathbb{C}\right) \land \left(\left(k \cdot a\right) \rvert \left(k \cdot b\right)\right) \land \left(k \neq 0\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4, 5, 6, 7
3	Operation	operator: 10 operands: 8
4	Operation	operator: 10 operands: 9
5	Operation	operator: 10 operands: 11
6	Operation	operator: 12 operands: 13
7	Operation	operator: 14 operands: 15
8	ExprTuple	23, 16
9	ExprTuple	25, 16
10	Literal
11	ExprTuple	24, 16
12	Literal
13	ExprTuple	17, 18
14	Literal
15	ExprTuple	24, 19
16	Literal
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	24, 23
21	Literal
22	ExprTuple	24, 25
23	Variable
24	Variable
25	Variable